Vehicle state estimation using a maximum likelihood based robust adaptive extended kalman filter considering unknown white Gaussian process and measurement noise signal

Robust adaptive smooth variable structure Kalman filter for spacecraft attitude estimation

In the extended Kalman filter (EKF) and the unscented Kalman filter (UKF) of non-linear system, the mathematical model and the noise statistics are essential; this limitation was settled by adaptive algorithm. The adaptive extended Kalman filter (AEKF) and adaptive unscented filter (AUKF) were proposed to solve the filtering problem of the system with unknown mathematical model or noise statistics in information fusion. The simulation result shows that the adaptive algorithm in EKF and UKF can improve the performance of filter and decrease the computing time.

In this work, the problem of battery state of charge estimation is investigated using a model based approach. An experimentally validated model of a battery developed by AllCell Technologies, specific for light electric vehicles (electric scooter or bicycles) is used. Two state of charge estimation algorithms are developed: an extended Kalman filter and an adaptive extended Kalman filter. The adaptive version of Kalman filter is designed in order to adaptively set a proper value of the model noise covariance, using the information coming from the on-line innovation analysis. A comparison between the two approaches is conducted that shows that the adaptive Kalman filter can deal with the problem of incorrect value of the model noise covariance matrix producing lower estimation error.

This paper presents a new robust adaptive unscented particle filtering algorithm by adopting the concept of the adaptive robust filtering to the unscented particle filter. This algorithm adaptively determines the equivalent weight function and adaptively adjusts the adaptive factor constructed from predicted residuals to resist the disturbances of singular observations and the kinematic model noise, thus preventing particles from degeneracy. It also uses the unscented transformation to improve the accuracy of particle filtering, thus providing the reliable state estimation for improving the performance of adaptive robust filtering. Experiments and comparison analysis demonstrate that the proposed filtering algorithm can effectively resist disturbances due to system state noise and observation noise, and the filtering accuracy is much higher than the extended Kalman filter, unscented Kalman filter, standard particle filter and unscented particle filter.

This study represents a method for estimating the state of charge (SOC) of lithium‐ion batteries using radial basis function (RBF) networks and square‐root unscented Kalman filter (KF). The RBF network is trained offline by sampled data from the battery in the charging process. This type of neural network finds the non‐linear relation which is required in the state‐space equations. The state variables include the battery terminal voltage and the SOC, at the previous sample and the present sample, respectively. The proposed method is tested experimentally on a lithium‐ion battery with 1.2 Ah capacity to estimate the actual SOC of the battery. The experimental results of the proposed method show some advantages, which include: (i) it is not very sensitive to determine, precisely, the measurement and process noise covariance matrices such as Kalman filter and (ii). It contains lower noise on the output, in comparison with Adaptive extended Kalman filter (EKF).

The problem of tracking with very long range radars is studied in this paper. First, the measurement conversion from a radar's r-u-v coordinate system to the Cartesian coordinate system is discussed. Although the nonlinearity of this coordinate transformation appears insignificant based on the evaluation of the bias of the converted measurements, it is shown that this nonlinearity can cause significant covariance inconsistency in the conventionally converted measurements (CM1). Since data association depends critically on filter consistency, this issue is very important. Following this, it is shown that a suitably corrected conversion (CM2) eliminates the inconsistency. Then, initialized with the converted measurements (using CM2), four Cartesian filters are evaluated. It is shown that, among these filters, the converted measurement Kalman filter with second order Taylor expansion (CM2KF) is the only one that is consistent for very long range tracking scenarios. Another two approaches, the range-direction-cosine extended Kalman filter (ruvEKF) and the unscented Kalman filter (UKF) are also evaluated and shown to suffer from consistency problems. However, the CM2KF has the disadvantage of reduced accuracy in the range direction. To fix this problem, a consistency-based modification for the standard extended Kalman filter (E1KF) is proposed. This leads to a new filtering approach, designated as measurement covariance adaptive extended Kalman filter (MCAEKF). For very long range tracking scenarios, the MCAEKF is shown to produce consistent filtering results and be able to avoid the loss of accuracy in the range direction. It is also shown that the MCAEKF meets the posterior Carmer-Rao lower bound for the scenarios considered.

For vehicle state estimation, conventional Kalman filters work well under Gaussian assumptions. Still, they are likely to degrade dramatically in the practical non-Gaussian situation (especially the noise is heavy-tailed), showing poor accuracy and robustness. This article presents an estimation technique based on the maximum correntropy criterion (MCC) combined with an adaptive extended Kalman filter (AEKF), and an extended Kalman filter (EKF) based on the MCC has also been studied. A lateral-longitudinal coupled vehicle model is developed, while an observer containing the state vectors such as yaw rate, sideslip angle, vehicle velocity and tire cornering stiffness is designed using easily available in-vehicle sensors and low-cost GPS. After analyzing the algorithmic complexity, the proposed algorithm is validated by sine steering input and double lane change driving scenarios. Finally, it is found that MCC combined with AEKF/EKF has stronger robustness and better estimation accuracy than AEKF/EKF in dealing with non-Gaussian noise for vehicle state estimation.

Estimating the state of charge (SOC) of Li-ion battery by the traditional extend Kalman filter (EKF), the unreasonable noise settings and inaccurate model parameters may decrease the accuracy. Here, an adaptive dual extended Kalman filter which can dynamically adjust the process noise covariance and battery model parameters is established by the second order RC model. The algorithm uses the EKF algorithm as the main body, fixes the measurement noise covariance, and adaptively adjusts the process noise covariance based on the maximum likelihood estimation criterion. Another Kalman filter (KF) is simultaneously used to estimate battery model parameter in real time to constitute a joint algorithm. In this paper, the charging and discharging experiments of lithium iron phosphate batteries are carried out. The SOC estimation by different adaptive adjustment strategies of noise covariance are compared and analyzed under actual operating condition. Meanwhile, the SOC under different aging conditions is also estimated and compared. The results show that the proposed joint algorithm has higher estimation accuracy, faster convergence speed and more extensive applicability.

This paper considers translational and rotational state estimation of vehicle handling dynamics using a non-linear robust filtering method. The robust method is needed to compensate the modelling errors which are caused by a combination of many factors such as: parameter uncertainties, model simplification and non-linearities; these inevitably compromise the filter performance. A non-linear Robust Extended Adaptive Kalman Filter (REAKF) is proposed, based on a six degree of freedom (6DOF) vehicle model. The model uncertainties are represented using an integral quadratic constraint method. Parameter adaptation is then included to further increase the accuracy of the filter; the tyre longitudinal and cornering stiffnesses are varied, since both of these parameters are central to the vehicle non-linearities. The filter is tested in both simulation and practice using data collected from a real vehicle. Comparisons are also made with the standard Extended Kalman Filter (EKF) and the non-adaptive Robust Extended Kalman Filter (REKF). The combination of evidence from both tests illustrates the performance and stability benefits of the REAKF.

In this paper, an adaptive unscented Kalman filter (AUKF) is developed for state estimation on a tractor-trailer system. For nonlinear systems, the unscented Kalman filter (UKF) is a well-known approach for observer design. Some research has shown the UKF can be more accurate than extended Kalman filter (EKF) with similar computation burden. However, the performance of traditional Kalman filter may deteriorate when process noise changes or sudden disturbance occurs due to the fixed process noise covariance (Q matrix) in the filter. An adaptive gain is calculated to compensate for the mismatch between the actual residual covariance and the deduced value from the filter, ensuring that the sequence of residual is uncorrelated. An estimated Q matrix is referred in the adaptive gain calculation at each sample. Simulation is done in various situations. The positions of trailer are used as measurements. Compared with the standard UKF (SUKF) and another adaptive UKF, the proposed algorithm has better result.

Combined Kalman and sliding innovation filtering: An adaptive estimation strategy

An adaptive Kalman filter algorithm is adopted to estimate the state of charge (SOC) of a lithium-ion battery for application in electric vehicles (EVs). Generally, the Kalman filter algorithm is selected to dynamically estimate the SOC. However, it easily causes divergence due to the uncertainty of the battery model and system noise. To obtain a better convergent and robust result, an adaptive Kalman filter algorithm that can greatly improve the dependence of the traditional filter algorithm on the battery model is employed. In this paper, the typical characteristics of the lithium-ion battery are analyzed by experiment, such as hysteresis, polarization, Coulomb efficiency, etc. In addition, an improved Thevenin battery model is achieved by adding an extra <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</i> branch to the Thevenin model, and model parameters are identified by using the extended Kalman filter (EKF) algorithm. Further, an adaptive EKF (AEKF) algorithm is adopted to the SOC estimation of the lithium-ion battery. Finally, the proposed method is evaluated by experiments with federal urban driving schedules. The proposed SOC estimation using AEKF is more accurate and reliable than that using EKF. The comparison shows that the maximum SOC estimation error decreases from 14.96% to 2.54% and that the mean SOC estimation error reduces from 3.19% to 1.06%.

The unscented Kalman filter (UKF) has become a popular alternative to the extended Kalman filter (EKF) during the last decade. UKF propagates the so called sigma points by function evaluations using the unscented transformation (UT), and this is at first glance very different from the standard EKF algorithm which is based on a linearized model. The claimed advantages with UKF are that it propagates the first two moments of the posterior distribution and that it does not require gradients of the system model. We point out several less known links between EKF and UKF in terms of two conceptually different implementations of the Kalman filter: the standard one based on the discrete Riccati equation, and one based on a formula on conditional expectations that does not involve an explicit Riccati equation. First, it is shown that the sigma point function evaluations can be used in the classical EKF rather than an explicitly linearized model. Second, a less cited version of the EKF based on a second-order Taylor expansion is shown to be quite closely related to UKF. The different algorithms and results are illustrated with examples inspired by core observation models in target tracking and sensor network applications.

Fast non-intrusive estimation of liquid-phase interface and boundary heat flux in participating media by the Kalman filtering methods

State of Charge (SOC) estimation plays a crucial role in managing the performance and longevity of electric vehicle (EV) batteries. Various estimation techniques, including various Kalman Filters (KF), have been employed for this purpose. The mathematical process and limits of different KF family algorithms are analysed. In this study, an impact of nonlinear KF parameters on SOC estimation accuracy for EV batteries is analyzed. Specifically, the performance of Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Particle Filter (PF) is examined. EKF is most preferred for SOC estimation whereas introducing sigma points in UKF is the basic difference between EKF and UKF. In comparison to EKF and UKF, PF is more flexible since it applies to nonlinear systems with non-Gaussian distributions. Utilising a sequence of noisy measurements, KF is a recursive method that approximates the state of a dynamic system. It requires accurate parameters such as process noise covariance (Q) and measurement noise covariance (R) to work effectively. In this work, the effect of these parameters on state of charge estimation using nonlinear KFs has been analysed under different settings of noise covariance matrices. Tuning these parameters is essential for optimizing the performance of the KF and ensuring accurate and reliable state estimation in real-world applications. To find parameter values that provide the best balance between accuracy, robustness, and computational efficiency, the tuning process involves experimentation, simulation, and validation using real-world data. According to the results observed, the filter parameters such as three diagonal elements of Q are selected as 2e-8, 0.005, 0.003 and R as 2e-6. By evaluating the state estimation accuracy under different driving scenarios, robustness and sensitivity of filtering technique in estimating SOC for EV batteries has been studied. This analysis contributes to the optimization of SOC estimation algorithms, enhancing the reliability and efficiency of EV battery management systems.